So I noticed we can define entropy in two very different ways:(adsbygoogle = window.adsbygoogle || []).push({});

1) quantum mechanically

[itex]S = -k Tr(\hat{\rho}\ln{(\hat{\rho})}) [/itex]

2) classically

[itex]S = -k \int \rho \ln{(\rho)} d\Gamma[/itex]

whereTris the trace and [itex]d\Gamma = \frac{1}{h^{3N}N!}\prod_{i}^{N} d^{3N}q_{i}d^{3N}p_{i}[/itex] is the phase space volume element.

My question is how summing over the diagonal of an operator is like integrating the same quantity over phase space.

Edit: I realise that we are working out a mean value.

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# Relationship between trace and phase space

Can you offer guidance or do you also need help?

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